European Frequency and Time Seminar (EFTS) quartz tuning fork laboratory session.

A quartz tuning fork packaged in a transparent casing is used to demonstrate

• closed loop oscillation using a Negative Impedance Converter (NIC) circuit (Allan deviation below $10^{-9}$ up to 30 s integration time).
• openloop stroboscopic imaging of the quartz prong motion driven by sound card output.

KiCAD board design files.

References:

Hardware (using a Raspberry Pi5 single board computer for running GNU Radio for controlling the sound card and recording the video stream):

• 32768 Hz tuning fork in transparent package: Epson FC-135 32.7680KA-AC5 (0.404 euros/p)
• sound card with sampling rate 96 kHz or higher, e.g. UGREEN (10.2 euros on amazon)
• "digital microscope" webcam, e.g. AmScope HHD Series (~50 euros)
• 7414 Schmitt trigger (0.5 to 0.7 euros)
• 7400 NAND gate (0.2 to 0.3 euros)

Note: the single board computer must be a RPi5 and not a RPi4 whose USB bus is too unstable to generate a clean audio signal probing the narrow tuning fork resonance. See the stroboscopy subdirectory for the demonstration.

Software

• use mplayer tv:// to display the webcam output (or vlc if it displays properly in the selected window manager): allows for stretching the image to full screen even if recording a "poor" webcam resolution (640x480) stream from the digital microscope.
• GNU Radio flowchart for driving the two channels of the stereo sound card (tested with GNU Radio 3.10) with 1 Hz offset between the signal driving the tuning fork and the stroboscopic signal driving the LED.
• Maybe wise to echo "performance" > /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor to run the CPUs at maximum speed (will heat to 65 degC).

Resources:

Equivalent BvD model of the quartz tuning fork (see the impedance analyzer measurement):

• R1=53727 $\Omega$
• L1=7221 H
• C1=3.268 fF
• C0=3.368 pF

Quality factor $Q=\frac{1}{R1}\sqrt{\frac{L1}{C1}}=27700$

Resonance frequency $f=\frac{1}{2\pi\sqrt{L1\cdot C1}}=\frac{1}{2\pi\sqrt{7221\times 3.268\cdot 10^{-15}}}=32763$ Hz